Discussion Papers in Accounting and Finance. Behind DEA Efficiency in Financial Institutions

Transcription

1 Discussion Papers in Accounting and Finance Behind DEA Efficiency in Financial Institutions C. Serrano Cinca University of Zaragoza, Spain C. Mar Molinero University of Southampton, UK and F. Chaparro García Universidad Autónoma de Bucaramanga, Colombia Number AF02-7 March 2002 ISSN

2 BEHIND DEA EFFICIENCY IN FINANCIAL INSTITUTIONS By: C. Serrano Cinca Department of Accounting and Finance University of Zaragoza, Spain. C. Mar Molinero Department of Management University of Southampton, UK. F. Chaparro García Department of Accounting Universidad Autónoma de Bucaramanga, Colombia This version: February 2002 JEL: G21 Address for correspondence: C. Serrano-Cinca: Department of Accounting and Finance, Fac. CC Económicas y Empresariales, Univ. Zaragoza, Gran Vía 2, Zaragoza (50.005) SPAIN serrano@posta.unizar.es Cecilio Mar Molinero s work was supported by a grant from the Ministerio de Ciencia y Tecnologia (Spain) under the Ramon y Cajal Programme.

3 BEHIND DEA EFFICIENCY IN FINANCIAL INSTITUTIONS ABSTRACT DEA has been extensively used to measure the efficiency of financial institutions. Its advantages are clearly understood. But there are many unresolved problems. There are various views based on different modelling philosophies of what constitutes inputs and outputs in a financial institution. The paper explores up to what point the various combinations of inputs and outputs are equivalent, and up to what point the efficiency score obtained by a given institution changes under the various combinations of inputs and outputs. The extent to which two institutions that achieve the same efficiency score arrive at it following different strategies is explored with the aim of finding out what is behind such a score. It is suggested that, not one but many different DEA specifications, containing different combinations of inputs and outputs, be modelled and that the results be analysed with the tools of multivariate statistics. Particular emphasis is placed on using tools that visualise the main characteristics of the data. By-products of the approach proposed here are the creation of league tables of financial institutions in terms of efficiencies and the possibility to assess strengths and weaknesses of individual institutions. This methodology is applied to the particular case of Spanish savings banks (Cajas de Ahorros) and proves to be particularly rewarding. KEY WORDS Efficiency, savings banks, Principal Component Analysis, banking, Data Envelopment Analysis. 3

4 BEHIND DEA EFFICIENCY IN FINANCIAL INSTITUTIONS 1. INTRODUCTION Efficiency is a key concept for financial institutions. It has long been studied. A review of 130 such studies in 21 countries is given by Berger and Humphrey (1997). Berger and Humphrey classify papers according to the technical approach employed, which they identify as parametric- Stochastic Frontier Approach (SFA), Distribution Free Approach (DFA), Thick Frontier Approach (TFA)- or non parametric- Data Envelopment Analysis (DEA), Free Disposal Hull (FDH), Index Numbers (IN), Mixed Optimal Strategy (MOS). By far the most popular technical approach is DEA, which was applied in 62 of the papers surveyed. DEA is appropriate for sets of homogeneous units with similar inputs and similar outputs since it performs multiple comparisons using a Linear Programming based approach. The assumptions are minimal. Inputs and outputs do not need to be measured in the same units, which adds to the advantages of the methodology. A survey of the more restricted area of DEA applications to bank branch performance is given by Schaffnit et al. (1997). Some recent references on the application of DEA to financial institutions are Dekker and Post (2001), Pastor et al. (1997), Hartman et al. (2001), Kuosmanen and Post (2001), Seiford and Zhu (1999), Saha and Ravisankar (2000), and Athanassopoulos (1997). For the purposes of this paper, it will be useful to make a distinction between model and specification in a DEA context. Different philosophical approaches as to what a financial institution does, and what is meant by efficiency will lead to different models; see Berger and Mester (1997) for a full discussion. Two basic models are prevalent in the literature: intermediation and production. Specification will refer to a more restricted concept: the particular set of inputs and outputs that enter into model definition. The variety of models and specifications for financial efficiency analysis is reflected in practice. The selection of inputs and outputs varies from study to study, giving an impression of confusion. For example; a particular item, such as deposits, may be treated as an input or as an output according to whether the institution is modelled from the point of view of production or from the point of view of intermediation, see Athanassoupoulos (1997). This is a matter of concern, as the level of efficiency of a financial institution may depend on the 4

5 particular choice of inputs and outputs. It may be puzzling for the manager of a bank branch to discover that it is possible for different researchers to arrive at different conclusions about the efficiency of a bank branch when using the same technique (DEA). However, this confusion may be more apparent than real, since alternative specifications may be equivalent and the case may never arise. The study of the extent to which two different specifications are equivalent is one of the purposes of this paper. Model and specification selection are not the only issues addressed in this paper. We wish to go behind the efficiency score. Two financial institutions may achieve the same DEA efficiency under a given model and under a common specification, but they may still be very different. Efficiency, being a mere score, may be compatible with a variety of management strategies. Imagine two institutions that achieve the same efficiency, one may have specialised in the production of a particular output and the other on the good use of a particular input. These differences will, of course, be reflected in different weight structures for inputs and outputs, and could be identified by means of such techniques as cross-efficiency analysis; Doyle and Green (1994). Here we propose a new methodological approach to strategy identification for financial institutions based on multivariate statistical analysis. This approach has the advantage of visualising the way in which a particular DEA score has been achieved by an institution and how this score is related to the model selected. In this paper, efficiencies are calculated for a variety of DEA specifications. It is proposed that DEA modelling be embedded in a multivariate statistical framework. This paper unfolds as follows. The next section contains a discussion of efficiency in financial institutions. The particular case study of Spanish savings banks (Cajas de Ahorros) is introduced and presented in the next section. This is followed by a description of the model and its implementation. The paper is completed with a conclusions section. 2. EFFICIENCY MODELLING IN FINANCIAL INSTITUTIONS For modelling purposes, financial institutions are seen from the point of view of intermediation or from the point of view of production; see Athanassoupoulos (1997). Under the intermediation model they collect deposits and make loans in order to make a profit. 5

6 Deposits and acquired loans are inputs. Institutions are interested in placing loans, which are traditional outputs in studies of this kind; see, for example Berger and Humphrey (1991). Under the production model, a financial institution uses physical resources such as labour and plant in order to process transactions, take deposits, lend funds, and so on. In the production model manpower and assets are treated as inputs and transactions dealt with -such as deposits and loans- are treated as outputs. See, for example, Vassiloglou and Giokas (1990), Schaffnit, Rosen and Paradi (1997), Soteriou and Zenios (1999). The mathematical models used to study the efficiency of financial institutions can be divided into two groups: those based on parametric frontier techniques, and those based on Data Envelopment Analysis (DEA). Berger and Humphrey find inconsistencies between the two approaches, although Ondrich and Ruggiero (2001) argue that both produce similar rankings, and conclude that there is no advantage in using parametric frontiers. In this paper we focus on DEA models. Up to what point different DEA modelling approaches produce different results? This question can only be answered by looking at particular case studies. Oral and Yolalan (1990) found that a DEA model aimed at estimating service efficiency in bank branches in Turkey produced indistinguishable results from an alternative DEA model focused on profitability. A way of out this problem, the one implemented in this paper, would be to develop specifications with many inputs and outputs. This would be an attempt to create a general model that encompasses various modelling philosophies as particular cases. But care has to be exercised since the more inputs and outputs a model contains, the more units become efficient through specialisation or, as Lovell and Pastor (1997) put it, because they are self-identifiers. The relationship between efficiency and the number of inputs and outputs has been studied by Pedraja Chaparro et al. (1999). Alternative specifications for inputs and outputs for a given model have been explored in many studies. Athanassopoulos (1997) observes a lack of consistency in the selection of inputs and outputs when studying bank branch efficiency. Oral and Yolalan (1990) experiment with various specifications and observe that efficiencies change according to the input/output mix chosen. Some times there is no choice, as the chosen specification is in part determined by the data that is available; Vassiloglou and Giokas (1990). Pastor and Lovell (1997) observe that alternative specifications may not give significantly different results, and apply the Ruiz Gomez et al. (2002) methodology to choose a parsimonious specification. This approach is based on a sound mathematical model, but has a mechanical feel to it. But 6

7 different specifications are not totally equivalent, and it is difficult to assess what are the consequences for individual units of adding or removing an input/output without engaging in considerable extra work. A new approach to specification search is proposed in this paper. The distinctive features of a specification are revealed by embedding DEA efficiency results into a multivariate statistical framework. We use in particular Principal Components Analysis (PCA), multiple regression, and Hierarchical Cluster Analysis (HCA). PCA has been used as an alternative to DEA by Zhu (1998) and Premachandra (2001). PCA as a data reduction technique to select inputs and outputs has been used by Adler and Golany (2001). In our approach, PCA plays a fundamental role in specification and model selection. We do not attempt to find a best specification of inputs and outputs. A variety of possible specifications that offer combinations of inputs and outputs are estimated and efficiencies calculated for each financial institution under each specification. In this way, a matrix is obtained in which each column corresponds to a specification, and each row to a financial institution. This matrix is analysed by means of Principal Components Analysis (PCA). Component scores are plotted to show the extent to which the efficiency of financial institutions remains unchanged under the various specifications. The plot is interpreted by means of property fitting (Pro-Fit), a regression-based technique. The superimposition of the Pro-Fit results on the scores plot will help to identify specification equivalence, guide model selection, identify outlying behaviour, and assess strategic behaviour patterns in financial institutions that achieve the same efficiency score. The methodology will be applied to the particular case of Spanish Savings Banks (Cajas de Ahorro). 3. A CASE STUDY: SPANISH SAVINGS BANKS Savings banks (Cajas de Ahorro) are key players in the Spanish financial system. They differ from traditional banks in their legal status, which obliges them to invest some of their profits into good causes such as supporting the arts or providing for the elderly. Savings banks in Spain tend to operate within specific geographical areas, although some of them have become national institutions. This local character is also reflected in their financial structures, which differ from region to region; see Serrano Cinca (1998) for a discussion of geography and financial success in this context. Wilkinson (2001) points out that Spanish Savings Banks are 7

8 very successful institutions, with none having defaulted since their creation over a century ago. They take 57% of all deposits, although traditional banks make more loans than they do. In recent years this sector has undergone an intense concentration process. Starting in 1980 there have been 34 mergers. Some other mergers are still under discussion. The largest institutions are Caja Madrid and La Caixa. The total number of Savings Banks is 47. There have been many empirical studies on the efficiency of Spanish financial institutions. Examples are Lozano-Vivas (1997 and 1998), Dietsch and Lozano-Vivas (2000), Lovell and Pastor (1997), Pastor (1999), and Pastor et al (1997). This section will be divided into sub-sections. First, the data set will be described. The second subheading will concentrate on DEA and PCA. Empirical results will be interpreted in the third and fourth sub-sections. 3.1 THE DATA SET: 3 inputs and 3 outputs Data was obtained from the Statistic Yearbook of the CECA (The Spanish Confederation of Savings Banks) on annual accounts published by all 47 Spanish Savings Banks for the year Having been extracted from annual accounts, all the data except number of employees, is measured in monetary units. The list of all institutions is given in Table 1. Rather than use the full name of each institution, the Domain Name of their web page has been employed to identify them. The full Internet address of each institution is of the form After a survey of the inputs and outputs used in the literature, the following inputs and outputs were selected. Input A: Input B: Input C: Output 1: Output 2: Output 3: Number of employees Fixed assets Deposits Operating Income Deposits Loans 8

9 There is much agreement on what constitutes inputs and outputs under the production model and under the intermediation model, although not all authors use the same set of inputs and outputs. The list displayed responds to a pragmatic use of available information. A source of debate relates to deposits, which could be seen as inputs or as outputs. See Pastor, Perez and Quesada (1997) for a discussion. Deposits are treated as inputs by Mester (1989), and Elyasiani and Mehdian (1992); they are treated as outputs by Berger and Humphrey (1991), and Ferrier and Lovell (1990); they are treated simultaneously as inputs and outputs by Aly et al (1990). The values of all inputs and outputs for all the Savings Banks are given in Table 1. Table 1 about here Notation will be introduced in order to simplify the discussion of the various specifications. Inputs are referred to by means of capital letters, in such a way that the first input is represented by the letter A, the second input by the letter B, and the third one by the letter C. Outputs are referred to by means of numbers. The first input is associated with number 1, the second input with number 2, and the third input with number 3. In this way a specification that treats a savings bank as an institution whose employees (input A) take deposits (output 2) and place loans in the market (output 3) would be labeled A23. If this specification is augmented with fixed assets (input B) and operating income (output 1), the specification becomes AB123. Specification AB123 treats a savings bank as a production unit that employs manpower (A) and plant (B) in order to generate income, deposits, and loans. An intermediation model would be described by a specification such as AC13, in which deposits (C) are treated as an input. Under this specification a savings bank is an institution whose employees collect deposits in order to make loans and generate income. Other possible views of the way in which a savings bank operates can be generated by using different combinations of inputs and outputs. Efficiency ratios are generated by choosing a specification with only one output and one input. It is, of course, possible to use all possible combinations of inputs with all possible combinations of outputs. The total number of specifications that could possibly be generated with n inputs and m outputs is given by the formula n i m * i= 1 i= C C where n 1 i m C i n n n! = = i i! ( n i)! 9

10 In general, it will not be necessary to calculate efficiencies under all possible specifications, as some of them can be discarded on a priori grounds. In our case there are 3 inputs and 3 outputs, giving a possible total number of specifications of 49. Specifications that treat deposits both as inputs and outputs have been excluded, reducing their total number to 33. The complete list of specifications and the inputs and outputs that they contain can be found in Table 2. Table 2 about here DEA efficiencies, on a scale from 0% to 100%, for all savings banks were calculated under Constants Returns to Scale (CRS) for all specifications. The results are given in Table 3. Table 3 about here Visual examination of Table 3 reveals some important features. Some savings banks (Cajavital, Bbk, Cajamadrid, Cajanavarra, Bancaja) are 100% efficient under many specifications. In the same way, some savings banks achieve low scores under most specifications. No savings banks is efficient under all specifications, highlighting the fact that the selection of inputs and outputs and, therefore, the view of what constitutes efficiency in the financial sector, is a matter of importance. This was one of the conjectures that guided this research. Take, for example, Bbk, which is 100% efficient under 12 specifications, implying that this is an excellent institution. However, its efficiency drops to 52% under B23. This suggests the presence of some weakness in Bbk, a subject that will be further explored below. A counter example is Cajaen, whose DEA scores tend to be low, but becomes 100% efficient under 4 specifications: BC1, BC13, ABC1, ABC13. This indicates that, although Cajaen can take action to improve its efficiency, it has some strong points that deserve further attention. Consider now the case of two institutions that achieve the same DEA score under a given specification. An example would be Bancaja and Cajavital. They both are 100% efficient under AB123. But differences appear if other specifications are considered. For example, under A123 Cajavital achieves 100% efficiency while the same score for Bancaja is 86%. Under specification B123 Cajavital is 63% efficient while Bancaja is 100% efficient. This 10

11 indicates that the two institutions follow two different paths to efficiency. What is behind their strategies? Answering such a question was another of the objectives of this research. In summary, the level of efficiency achieved by a particular financial institution depends on the chosen specification, indicating that specification search is delicate and important. In addition, if two financial institutions achieve the same efficiency score under a given specification they may do so following very different patterns of behavior: there is no single path to efficiency in financial institutions. Exploring what is behind a DEA score is the objective of the next three subsections. 3.2 DEA SPECIFICATION SEARCHES USING MULTIVARIATE METHODS Although visual inspection of Table 3 is a source of important insights, a more formal analysis of the information it contains will be performed. Table 3 will be treated as a matrix with 47 cases, the savings banks, and 33 variables, the specifications, and analyzed using multivariate statistical methods. The methodological approach will combine PCA, HCA, and Pro-Fit. The results of applying PCA to Table 3 are shown in Table 4. Four eigenvalues take values larger than one, accounting for 96% of the total variance. The first principal component accounts for 47% of the variance. The second principal component is also of importance, as it accounts for a further 21%. The variance accounted for drops to 18% in the case of the third component, and to 10% in the case of the fourth component. Component loadings are given in Table 5. In what follows the discussion will be based on these four components. Table 4 about here Table 5 about here Component scores were calculated for each savings bank. The plot of the first and second component loadings for each savings bank is shown in Figure 1. The plot of the third and fourth component loadings for each savings bank is shown in Figure 2. 11

12 Figure 1 about here Figure 2 about here Those savings banks that achieved full 100% efficiency under a majority of specifications (Cajanavarra, Cajamadrid, Cajavital, Kutxa, Bbk) plot towards the right hand side of Figure 1. Those savings banks that consistently underperform plot towards the left hand side of this same figure. It is to be noticed that Caixacarlet, the only institution that no longer exists, having been taken over by Bancaja in July 2001, is located at the extreme of the left hand side. It is, therefore, clear that the first principal component can be interpreted as a global efficiency score. An efficiency ranking of savings banks can be obtained by simply looking at the ordering on the first component. Usually, efficiency rankings are based on the concept of super-efficiency introduced by Andersen and Petersen (1993), although other ranking methods have also been proposed; Doyle and Green (1994), Sinuany-Stern and Friedman (1998), and Raveh (2000). The advantage of the ranking procedure proposed here is that it embeds results from many different specifications, while the alternatives produce a ranking for each specification. Concentrating now on the second component, the North-South direction in Figure 1, it can be observed that Bancaja plots towards the top of the figure, while Cajavital plots towards the bottom. Both are 100% efficient under many specifications. In which way they are different, and what accounts for their achieving full efficiency, will be revealed by attaching meaning to the second principal component. In the same way, interpretation of the position of savings banks in Figure 2 requires that meaning be attached to the third and the fourth principal components. A standard way of attaching meaning to principal components is to analyze component loadings. These are given in Table 5. It can be seen there that all loadings associated with the first component are positive, supporting the view that this component gives an overall measure of efficiency. First component loadings are high for all specifications that exclude input C (deposits). Amongst those specifications that include input C only those which also include inputs A and B achieve high first component loadings. The specifications that achieve the highest first component loadings are AB13, AB123, and AB12. If a combination of inputs 12

13 and outputs were to be selected in order to produce a global assessment of efficiency, any of these three models would be appropriate. Specifications that include deposits as an input (C) are salient in the second component, in the sense that they achieve high positive component loadings. The third component appears to be associated with fixed asset utilization (input B), and the fourth one with operating income (output 1). These results can be visualized by means of Pro-Fit and Cluster analysis. This will be done in the next subsection. 3.3 RESULTS VISUALIZATION AND STRATEGIC PATTERN IDENTIFICATION Each specification generates a DEA score for each savings bank, and each savings bank is located in Figures 1 and 2 by means of its component scores. The relationship between DEA scores and component scores can be assessed by means of regression analysis and visualized. For each specification, a regression was run in which the dependent variable was the efficiency value, and the independent variables were the four component scores. Each institution was treated as a case in the regression. In total, 33 regressions were performed. This procedure is known as Property Fitting (Pro-Fit) analysis; see Schiffman et al (1981). For a given specification, Pro-Fit produces a directional vector on Figures 1 and 2 in such a way that DEA efficiencies grow in the direction of the vector. Directional vectors were calculated for each one of the 33 specifications. Being regression-based, the quality of the representation can be assessed by means of the coefficient of determination, R 2, and the F statistic. These are shown in Table 6. It is to be noticed that values of R 2 are very high, all of them above 0.90, indicating that there is a strong linear relationship between DEA scores and the position of the savings bank in Figures 1 and 2. The directional vectors are located in Figure 1 and 2 by means of their directional cosines, which are related to the regression coefficients. The value of their standardized directional cosines, -γ 1, γ 2, γ 3, and γ 4 - and their level of significance, are also shown in Table 6. Pro-Fit vectors have been superimposed on component plots in Figures 3 and 4. 13

14 Table 6 about here Figure 3 about here Figure 4 about here If efficiencies produced by two different specifications are highly correlated, their associated Pro-Fit vectors will plot next to each other. In the same way, if the efficiencies generated by particular specifications are highly correlated with a particular principal component score, the Profit vector will plot in the direction of the axis associated with the given component. The length of the projection of the Pro-Fit vector reflects its relevance in the interpretation of the particular figure. The longer the vector, the more agreement there is between the ordering of the savings banks in the representation and the efficiency values obtained from the specification. Pro-Fit vectors form a fan in Figure 3. All vectors point in the direction in which efficiency grows. There are 33 specifications, which means that there are 33 definitions of efficiency. Most vectors point in the direction of the first principal component. This confirms the observation that the first principal component gives an overall measure of the efficiency of a savings bank, and that an ordering along the first principal component produces an efficiency ranking of institutions. A small set of vectors is clearly associated with the second principal component, as they all point towards the top of Figure 3. All such vectors contain deposits as an input, reflecting the fact that the value of the second principal component score is influenced by the decision to model deposits as an input. In other words, amongst the 33 specifications, those that include deposits as an input are a group apart from the rest. Similar considerations would relate the value of the third principal component to the decision to use specifications that contain as a sole input the value of fixed assets (B), since a fan that includes only B as an input can clearly be discerned on the left hand side of Figure 4. Finally, in Figure 4 it can be seen that the fourth principal component discriminates between specifications that operating income as an output (output 1) and those that do not contain it. It 14

15 is clear that vectors that contain output 1 in their definition point towards the bottom of Figure 4, while those that do not contain output 1 in their definition point towards the top of the figure. All the above discussion has been based on the interpretation of two dimensional projections of a four dimensional data set. Each Pro-Fit vector is plotted in a four dimensional space, and it would be appropriate to assess if the groups that are observed on the projections are true reflections of the groups that exist in the space. For this reason Pro-Fit analysis has been supplemented with Hierarchical Cluster Analysis (HCA). If equivalent specifications exists, they will group into clusters, and if specifications within a cluster share something in common, the analysis will reveal it, with the added bonus that model simplification will naturally follow. Efficiencies in Table 3 have been taken as inputs for HCA and clustered using Ward s method with Euclidean distances. This method maximizes within group homogeneity and between group heterogeneity. The dendrogram can be seen in Figure 5. Figure 5 about here Specifications group neatly into three clusters in Figure 5. These clusters have been superimposed in Figure 3 and have been labeled I, II, and III. Cluster I is located at the North and North West of Figure 3, grouping specifications whose Pro-Fit vectors point up or up and to the right of the figure. All the specifications in cluster I contain deposits as input (C). It includes specifications of the type C, AC, BC, or ABC. Deposits as an input are a standard feature of intermediation models. Cluster II is located to the right of Figure 3, above the first principal component. It is formed by specifications that contain a single input, fixed assets (B). Cluster III is located on the right hand side of figure 3, towards the bottom of the first principal component. It groups specifications that do not contain deposits as an input, only A (number of employees) or AB (number of employees and fixed assets). Clusters II and III group specifications that can be associated with production type models. Clusters II and III group together at a higher level of clustering. 15

16 It can be argued that specifications contained in a given cluster are largely equivalent in the sense that they produce similar efficiency scores for the various savings banks. This can guide input and output selection. Each cluster can be represented by a single specification, reducing the total number of possible specifications from 33 to 3. The selected specification could be the most parsimonious one or the most central one within the cluster. The superimposition of HCA and Pro-Fit results on the component score map clearly reveals the differences between the various modeling approaches. The decision to opt for an intermediation model or for a production model, which is related to the way in which deposits are treated in the specification, will impact on the efficiencies obtained for individual saving banks. Since Cluster I is clearly associated with the second principal component and clusters II and III are clearly associated with the first principal component, different views of the world will, in general, lead to different assessments of efficiency and to different calls for action. This leads to the conclusion that if we want to study the efficiency of a savings bank, we should not proceed by choosing only one model and only one specification, as this may miss important features of its operations. 3.4 LOOKING BEYOND THE EFFICIENCY SCORE It has been argued that there is no single definition of efficiency in the context of savings banks. Different views of the way in which savings banks operate, as reflected in the different modeling philosophies will produce different efficiency scores. The combination of PCA, Pro-Fit, and HCA sheds light into the reasons why a particular savings bank achieves a certain efficiency level. This subject will be further examined in what follows. Take Bancaja and Cajavital, two previously discussed institutions. They both achieve 100% efficiency under 11 specifications: AB1, AB12, AB123, AB13, AB23, AB3, AC13, AC3, ABC1, ABC13 and ABC3. They both appear on the extreme right hand side of the first principal component in Figure 1. They would both come at the top of an efficiency ranking based on the first principal component. We could just conclude that they are excellent institutions and leave it at that. But it is also to be noticed that under specifications A1, A12, A123, A13, A23, A2, A3, and AB2 Cajavital is 100% efficient but not Bancaja. The Pro-Fit lines associated with all these specifications point towards the negative of the second principal 16

17 component in Figure 3. All these specifications contain number of employees (A) in their definition, which leads to the conclusion that Cajavital owes its position in the league table to the good performance of its employees. The specifications that make Bancaja is 100% efficient but not Cajavital can be divided into two groups. The first group contains C13, C3, BC13, BC1, and BC3 whose associated Pro-Fit lines point directly upwards, in the direction of the second principal component. All these contain Deposits as an input, and are specifications that would be developed under the intermediation modeling philosophy. The second group contains specifications B1, B12, B123, B13, B23, and B3, all of them belonging to Cluster II and containing fixed assets (B) in their definition. One can conclude that Bancaja s strong point is an efficient utilization of its fixed assets, and that Bancaja is a good institution from the intermediation point of view. This discussion can be extended to the differences and similarities of Bancaja and Cajavital under the third and fourth principal components. Cajavital is located on the positive side of the third principal component, while Bancaja is located on the negative side of this component. Recall that the third principal component is associated with fixed assets (input B), we observe that the use of fixed assets discriminates between the two institutions, a conclusion that has already been arrived at by means of Cluster analysis. The fourth principal component, associated with operating income (output 1), shows little difference between these two savings banks. Systematic analysis of Figures 1 and 2, together with the interpretations provided in Figures 3 and 4 makes it possible to assess the global efficiency of an institution and the strategies under which such global efficiency was achieved. Strengths and weaknesses become apparent. Take, for example, a previously mentioned case: Cajaen. In Figure 1 it plots towards the center of the first component, indicating that its global efficiency is mediocre. In is also located at the top of the second principal component, which is associated with is consistent with being 100% efficient under specifications BC1, BC13, ABC1, and ABC13, all of them belonging to Cluster I and considering deposits as an input, and implying that Cajaen would be only identified as efficient under an intermediation approach. In Figure 2 Cajaen is located towards the most negative side of the fourth principal component. Cajaen would be identified as strong in specifications that include operating income as an output. Finally, Bbk, appears on the extreme right hand side of the Figure 1, implying that it is an efficient savings bank from the global point of view. Its location in this figure is consistent with an efficient use of human resources (input A). In Figure 2, Bbk is also located towards the extreme right hand 17

18 side, on the lower half of the figure. We notice that in Figure 4, vectors associated with specifications that contain fixed assets (input B) point on the whole towards the left hand side. This implies that Bbk under performs in specifications that contain fixed assets as an input, something that is coherent with the results shown in Table 3. 4 CONCLUSIONS There has been much interest and debate on how to model DEA efficiency in financial institutions. This has extended over the type of model (intermediation or production) that is appropriate, as well as to the selection of inputs and outputs once a modeling philosophy has been selected. We have suggested a specification search strategy that highlights the extent to which two different DEA specifications produce similar results and the reasons why this happens. The methodology proposed relies on estimating a variety of input/output mixtures and analyzing the results by means of multivariate statistical methods. Particular emphasis is given to data visualization, which is achieved by combining Principal Components Analysis, Property Fitting, and Hierarchical Cluster Analysis. This approach has been applied to the particular case of Spanish savings banks. Three different views of what constitutes efficiency in a savings bank have been identified, although these can be further grouped into two that are related to the intermediation and the production models. The treatment of deposits as an input or as an output has proven to be key in the modeling of financial institutions. The standard procedure of starting by an a priori view of what inputs and outputs should go into the calculation of efficiency should be revised, as different models and specifications can produce different efficiency results for a given institution. A more realistic view would be to accept that efficiency is a multidimensional concept, and that several models ought to be estimated and combined before managerial action is taken to improve the way in which a financial institution works. Framing DEA results in a multivariate statistical context has allowed us to go behind efficiency as a mere score. It has been possible to offer a global view of the efficiency of an 18

19 institution which encompasses many specifications; it has made it possible to assess why a particular institution has achieved a given level of efficiency under a given choice of inputs and outputs; and has allowed to identify the various paths to efficiency followed by different institutions which would, under most studies, have been classified as equivalent but that differ in important aspects of their operations. Further advantages of the method proposed here is that it creates a natural ranking of institutions in terms of efficiency, and that it highlights the strengths and weaknesses of each institution. REFERENCES Adler, N., and Golany, B. (2001): Evaluation of deregulated airline networks using data envelopment analysis combined with principal component analysis with an application to Western Europe European Journal of Operational Research, 132 (2), Aly, H., Grabowsky, R., Pasurka, C., and Rangan, N. (1990): Technical, scale, and allocative efficiencies in U.S. banking: an empirical investigation, Review of Economics and Statistics, 72, Andersen P,. and Petersen N.C. (1993): A procedure for ranking efficient units in data envelopment analysis. Management Science, 39, Athanassopoulos, A.D. (1997): Service quality and operating efficiency synergies for management control in the provision of financial services: Evidence from Greek bank branches, European Journal of Operational Research, 98 (2), Berger, A.N., and Humphrey, D.B., (1991): The dominance of inefficiencies over scale and product mix economies in banking. Journal of Monetary Economics, 28, Berger, A.N., and Humphrey, D.B., (1997): Efficiency of financial institutions: International survey and directions for future research. European Journal of Operational Research, 98 (2), Berger, A.N., and Mester, L.J., (1997) Inside the black box: what explains differences in the efficiencies of financial institutions? Journal of Banking and Finance, 21, Dekker, D., and Post, T. (2001): A quasi-concave DEA model with an application for bank branch performance evaluation, European Journal of Operational Research, 132,

20 Dietsch, M., and Lozano-Vivas, A. (2000): How the environment determines banking efficiency: A comparison between French and Spanish industries, Journal of Banking & Finance, 24 (6), Doyle, J., and Green, R. (1994): Efficiency and cross-efficiency in DEA: derivations, meanings and uses. Journal of the Operational Research Society, 45, Elyasiani, E., and Mehdian, S. (1992): Productive efficiency performance of minority and nonminority owned banks: a nonparametric approach. Journal of Banking and Finance, 16, Ferrier, G., and Lovell, C.A.K. (1990): Measuring cost efficiency in banking: econometric and linear programming evidence, Journal of Econometrics, 46, Hartman, TE.; Storbeck, JE.; Byrnes, P. (2001): Allocative efficiency in branch banking. European Journal of Operational Research, 134, Kuosmanen, T.; Post, T. (2001): Measuring economic efficiency with incomplete price information: with an application to European commercial banks. European Journal of Operational Research, 134, Lovell, C.A.K., and Pastor, J.T. (1997): Target setting: an application to a bank branch network. European Journal of Operational Research, 98, Lozano-Vivas, A. (1997): Profit efficiency for Spanish savings banks, European Journal of Operational Research, 98, Lozano-Vivas, A. (1998): Efficiency and technical change for Spanish banks, Applied Financial Economics, 8, Mester, L.J. (1989): Testing for expense preference behaviour: mutual versus stock savings and loans. Rand Journal of Economics, 4, Ondrich, J., Ruggiero, J. (2001): Efficiency measurement in the stochastic frontier model. European Journal of Operational Research, 129, Oral, M., Yolalan, R. (1990): An Empirical Study on Measuring Operating Efficiency and Profitability of Bank Branches, European Journal of Operational Research, 46, Pastor, J.M. (1999): Efficiency and risk management in Spanish banking: A method to decompose risk, Applied Financial Economics, 9, Pastor, J.T., and Lovell, C.A.K. (1997): Target setting in a bank branch network, European Journal of Operational Research, 98, Pastor, J.M., Perez, F., and Quesada, J. (1997): Efficiency analysis in banking firms: An international comparison. European Journal of Operational Research, 98,

21 Pedraja Chaparro, F., Salinas Jimenez, J., and Smith, P. (1999): On the quality of the Data Envelopment Analysis model. Journal of the Operational Research Society, 50, Premachandra, I.M. (2001): A note on DEA vs principal component analysis: An improvement to Joe Zhu's approach, European Journal of Operational Research, 132, Raveh, A. (2000): The Greek banking system: reanalysis of performance. European Journal of Operational Research, 120, Ruiz Gomez, J.L., Pastor, J., and Sirvent, I. (2002): A statistical test for radial DEA models. Operations Research, forthcoming. Saha, A., and Ravisankar, T.S. (2000): Rating of Indian commercial banks: A DEA approach, European Journal of Operational Research, 124, Schaffnit, C., Rosen, D., and Paradi, J.C. (1997): Best practice analysis of bank branches: An application of DEA in a large Canadian bank, European Journal of Operational Research, 98 (2), Seiford, L.M. and Zhu, J. (1999): Profitability and marketability of the top 55 U.S. commercial banks Management Science, 45 (9), Serrano-Cinca, C. (1998): From Financial Information to Strategic Groups - a Self Organizing Neural Network Approach, Journal of Forecasting, 17, Schiffman, J.F., Reynolds, M.L. and Young, F.W. (1981): Introduction to Multidimensional Scaling: Theory, Methods and Applications. Academic Press, London. Sinuany-Stern Z., and Friedman L. (1998): DEA and the discriminant analysis of ratios for ranking units. European Journal of Operational Research, 111, Soteriou, A. and Zenios, S.A. (1999): Operations, quality and profitability in the provision of banking services, Management Science, 45 (9), Vassiloglou, M. and Giokas, D., (1990): A study of the relative efficiency of bank branches: An application of data envelopment analysis, The Journal of the Operational Research Society, 41, Wilkinson, E (2001): Savings banks are here to stay, Euromoney, 386, Zhu, J. (1998): Data envelopment analysis vs. principal component analysis: An illustrative study of economic performance of Chinese cities European Journal of Operational Research, 111,

22 Savings Bank Number of Fixed Operating Deposits Loans employees assets income Bancaja 4,551 37,346 97,758 1,907,234 2,147,534 Bbk 2,511 50,694 73,195 1,666,972 1,088,115 Cai 1,225 16,940 29, , ,491 Caixacarlet 83 1, ,844 20,789 Caixacatalunya 4,801 78,376 93,586 2,486,395 2,276,395 Caixagalicia 3,425 49,775 76,554 1,660,766 1,305,776 Caixagirona 756 6,952 13, , ,493 Caixalaietana ,886 13, , ,953 Caixamanlleu 380 4,414 6, , ,931 Caixamanresa 583 4,893 11, , ,761 Caixanova 2,299 32,465 50,584 1,027, ,264 Caixaontinyent 218 2,288 2,916 57,378 61,413 Caixapenedes 1,903 35,147 33, , ,034 Caixasabadell 1,245 13,951 19, , ,653 Caixatarragona 1,164 8,347 18, , ,479 Caixaterrassa 1,090 8,884 17, , ,650 Cajabadajoz ,030 13, , ,024 Cajacanarias 1,044 9,948 25, , ,342 Cajacantabria ,265 21, , ,316 Cajacirculo ,800 12, , ,653 Cajadeavila 578 7,622 12, , ,912 Cajadeburgos ,732 18, , ,792 Cajaduero 2,459 41,204 38,291 1,203, ,224 Cajaen 133 1,130 2,154 37,180 33,609 Cajaespana 2,666 48,512 58,120 1,275, ,839 Cajaextremadura 1,063 10,269 17, , ,454 Cajagranada 2,049 24,293 32, , ,897 Cajaguadalajara 233 2,242 3,460 82,167 69,047 Cajamadrid 10, , ,763 6,287,709 5,981,043 Cajamurcia 1,510 20,055 34, , ,753 Cajanavarra 1,369 13,398 31, , ,661 Cajarioja 411 5,422 7, , ,420 Cajasanfernando 2,084 21,750 30, , ,226 Cajasegovia 524 9,896 10, , ,685 Cajastur 1,324 16,302 32, , ,704 Cajasur 2,210 31,473 40, , ,895 Cajavital ,961 19, , ,498 Cam 5,031 59,676 97,589 2,106,343 2,022,398 Ccm 2,179 31,808 37, , ,599 Colonya ,030 23,857 18,896 Elmonte 1,982 24,431 38, , ,766 Ibercaja 4,241 43,135 68,216 1,789,422 1,478,053 Kutxa 1,654 38,807 47,738 1,100, ,668 Lacaixa 19, , ,928 7,885,253 7,199,949 Lacajadecanarias ,351 19, , ,800 Sanostra 1,412 18,545 22, , ,561 Unicaja 4,510 59,741 77,010 1,596,091 1,238,335 Table 1: List of savings banks and the values of inputs and outputs. 22

23 Model INPUT OUTPUT A1 Employees Income A12 Employees Income, Deposits A123 Employees Income, Deposits, Loans A13 Employees Income, Loans A23 Employees Deposits, Loans A2 Employees Deposits A3 Employees Loans B1 Assets Income B12 Assets Income, Deposits B123 Assets Income, Deposits, Loans B13 Assets Income, Loans B23 Assets Deposits, Loans B2 Assets Deposits B3 Assets Loans AB1 Employees, Assets Income AB12 Employees, Assets Income, Deposits AB123 Employees, Assets Income, Deposits, Loans AB13 Employees, Assets Income, Loans AB23 Employees, Assets Deposits, Loans AB2 Employees, Assets Deposits AB3 Employees, Assets Loans C1 Deposits Income C13 Deposits Income, Loans C3 Deposits Loans AC1 Employees, Deposits Income AC13 Employees, Deposits Income, Loans AC3 Employees, Deposits Loans BC1 Assets, Deposits Income BC13 Assets, Deposits Income, Loans BC3 Assets, Deposits Loans ABC1 Employees, Assets, Deposits Income ABC13 Employees, Assets, Deposits Income, Loans ABC3 Employees, Assets, Deposits Loans 23

24 Table 2: The 33 specifications and their definitions 24

25 A1 A12 A123 A13 A23 A2 A3 B1 B12 B123 B13 B23 B2 B3 AB1 AB12 AB123 AB13 AB23 AB2 AB3 C1 C13 C3 AC1 AC13 AC3 BC1 BC13 BC3 ABC1 ABC13ABC3 Bancaja Bbk Cai Caixacarlet Caixacatalunya Caixagalicia Caixagirona Caixalaietana Caixamanlleu Caixamanresa Caixanova Caixaontinyent Caixapenedes Caixasabadell Caixatarragona Caixaterrassa Cajabadajoz Cajacanarias Cajacantabria Cajacirculo Cajadeavila Cajadeburgos Cajaduero Cajaen Cajaespana Cajaextremadura Cajagranada Cajaguadalajara Cajamadrid Cajamurcia Cajanavarra Cajarioja Cajasanfernando Cajasegovia Cajastur Cajasur